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In your scenario how is the local made $100 item bought at $80? Where is a $20 refund paid from? You are double spending it on both imported and local goods
In the scenario local good is still worth $100 but given that you refund all good by the amount added by the tariff later, you have $20 refunded (not really $20 as i tried to show previously, but
$20 x total_tariff / total_amount_of_good_bought_locally_and_imported
, so somewhere between $80 and $100 net for local production and between $100 and $120 for imported good, depending on the ratioimport/import+localprod